Existence and uniqueness of positive solutions for a BVP with a p-Laplacian on the half-line

Abstract

In this work, we consider the second order multi-point boundary-value problem with a p-Laplacian $$displaylines{ ( ho(t)Phi_p(x'(t)))'+f(t, x(t), x'(t))=0,quad tin [0,+infty),cr x(0)=sum_{i=1}^{m}alpha_i x(xi_i), quad lim_{toinfty}x(t)=0,. }$$ By applying a nonlinear alternative theorem, we establish existence and uniqueness of solutions on the half-line. Also a uniqueness result for positive solutions is discussed when $f$ depends on the first-order derivative. The emphasis here is on the one dimensional p-Laplacian operator.

Keywords

• Multi-point boundary-value problem
• p-Laplacian
• half-line
• positive solutions
• existence
• uniqueness